Vibrations: The movement of an object in a back and forth manner. The object even at molecular level is moving in a wiggling motion causing the object to oscillate. This motion is what creates the movement of vibration. Vibration can be considered as an object being displaced out of equilibrium and passing back and forth over the original position.
Periodic Motion: Periodic motion is when an object goes under a repetitive, and constant motion. Periodic motion also deals with periods which is a length of time measured for the completion of an object's routine motion. This can be expressed as T in units and is 1/ frequency mathematically. Frequency of the periods, or the amount of times the object completes a period is called the frequency, and it can be measured by frequency = 1/period. Also within periods are amplitudes that express the maximum and minimum displacement of the object.
Simple Harmonic Motion: A motion in which acceleration of vibrating object is directly proportional to displacement and is always the same distance from the origin.
Such as the SHM spring above ^.
Pendulum Motion: The combination of centripetal force, GPE, and kinetic energy acting on an object with forces from weight and tension. Pendulum motion consists of the object moving in constant oscillation where there would be displacement horizontally as well as vertically for GPE and KE. One of the factors in pendulum motion is that the object is at it's fastest point of velocity at the bottom of the pendulum. Period of a pendulum can be measured by one complete movement of an object when the displacement returns back to 0. The object starts at the origin moves towards one side back to origin another side and back to origin. This is considered one period.
Hookes Law: The mass and the distance that the object stretches the spring is proportional to each other.
Waves:
Transverse Wave: particles of medium move in a perpendicular direction that the wave moves
Longitudinal Wave: particles of medium move in a parallel direction that the wave moves
Surface Wave: particles of medium move in a circular motion.
Electromagnetic Wave: Does not require a medium to transfer its energy.
Mechanical Wave: Does require a medium to transfer its energy.
Properties of Mechanical Waves: There are certain properties and terms that waves have, first is the crest which signifies the waves greatest amplitude, or where it has the greatest energy. The trough is the opposite, and is the position that has the least energy. Waves also deal with frequency and periods that was discussed earlier but have different equations. Wave Length is measured by 3 nodes where both crest and trough are present to create the wavelength measurement. Speed or the disturbance of the wave is measured by distance/time or frequency * wavelength,
Behavior of Waves:
Reflection: The wave bounces off of the boundary and moves in the angle of the intersection of the motion of the wave and the plane of the object.
Refraction: When the wave changes medium and most often takes on different speeds and direction.
Diffraction: When the wave hits a boundary and goes around it to conform to the shape of the object. The wave can also go through an opening and opens out in a cone shape spreading out evenly.
Interference: When 2 waves meet, it can cause either a constructive or destructive interference. Constructive interference creates a sum or a greater amplitude when the 2 waves meet. Destructive interference reduces the amplitude of the waves and creates a smaller wave when the 2 waves meet.
Doppler Effect: The doppler effect is a common phenomenon in our everyday life. An example would be a fast race car which has a distinct sound going from high to low pitch when the cars pass by. This occurs because the waves build up in front of the sound source because it is moving fast, so the observer hears a distorted sound when they are far away. The observer regains the normal sound when the car becomes closer because they don't have build up waves near or around the sides of the cars. Lastly the sound is lower as the car moves by because the sound is lagging behind causing less frequent waves.
Calculations:
We used the distance that the weight had stretched the spring as well as the weight for a force. Weight is calculated by 0.05 * 9.8. The force is only weight because we can only calculate that value. The distance is quantitative data that we have gathered.
Conclusion:
The relationship between distance and force is a linear relationship. It can be proven by our R^2 value of 0.999% making it a linear fit.The values or the slopes of the linear graph is the spring force constant. This is because of the formula from hooke's law. The differences between the two lines are that they have different spring force constants which changes the slope of the graphs. Objective:
To find the relationship between wave speed and frequency.
To find the relationship between wave speed and wavelength.
To distinguish between transverse and longitudinal waves.
Hypotheses: _
_The spring will move directly proportional as more mass is added.
_
Materials: _
Procedure: Part I – Marking the floor
Place strips of masking tape approximately .75m long on the floor at 0.0 m, 5.0 m and 10.0 m.
Mark and label a heavy ink/pencil line in the center of the tape at 0m.
Mark and label lines 10.0 cm, 20.0 cm and 30.0 cm to the left and right of your center mark on each.
Part II – Making a transverse pulse
Stretch your spring between the 0.0 m and 5.0 m tape marks on the floor with the rope loops around your wrist being located about 0.5 m beyond the tape marks on the floor.
Move your hand back and forth at right angles to the stretched spring until you can produce a pulse that travels down only one side of the spring (that is, the bump on the spring due to the pulse is only on the right or left side of the spring).
Send a pulse down the spring that has an amplitude of 10.0 cm. Have the third member of your group time the pulse as it travels from 0.0 m to 5.0 m.
Repeat steps #8-11 for pulses having amplitudes of 20.0 cm and 30.0 cm.
Repeat steps # 8-11 for 10-m distance.
Table 1 - Speed of pulses (Spring A)
5.0 meter total distance
10.0 meter total distance
Amplitude (cm)
10.0
20.0
30.0
10.0
20.0
30.0
Trial 1 time (s)
0.59
0.44
0.39
0.41
0.45
0.31
Trial 2 time (s)
0.6
0.53
0.35
0.31
0.43
0.35
Trial 3 time (s)
0.6
0.52
0.35
0.32
0.49
0.33
Avg.time (s)
0.597
0.497
0.363
0.347
.457
.33
Distance (m)
5.0
5.0
5.0
10.0
10.0
10.0
Avg. Speed (m/s)
.1194
.0994
.0726
.0347
.0457
.033
Repeat steps # 8-11 for a more tightly coiled spring.
Table 2 - Speed of pulses (Spring B)
5.0 meter total distance
10.0 meter total distance
Amplitude (cm)
20.0
30.0
40.0
20.0
30.0
40.0
Trial 1 time (s)
1.11
0.91
0.88
1.04
1
1.02
Trial 2 time (s)
1.127
0.89
0.87
1.03
0.95
1.01
Trial 3 time (s)
0.977
0.94
0.76
1.02
1
0.99
Avg.time (s)
1.0713
.913
.837
1.03
0.98
1
Distance (m)
5.0
5.0
5.0
10.0
10.0
10.0
Avg. Speed (m/s)
0.2147
0.1928
0.1742
0.103
0.098
0.1
Calculations: Added 3 quantitative data points and got the average. We found average speed by dividing the average time by distance. AvSpeed = avg time / distance. Part III – Making a longitudinal pulse
Make sure that the rope loops at the end of the springs are around your wrist. With your free hand, grasp the stretched spring about a meter from one end. Pull the meter of spring together toward yourself and then release it, being careful not to let go of the fixed end with your other hand! Another way to do this is to push the spring towards your lab partner and quickly bring it back to your original position.
Repeat several times. Note several observations:
_ Discussion Questions
How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance?
The speed of the waves do not change too much. It seems to be relatively similar.
Did amplitude influence the speed of the waves for the 5.0 meter distance?
No it didn't influence the speed of the wave.
How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance?
The speed of 3 different amplitudes don't change.
Did amplitude influence the speed of the waves for the 10.0 meter distance?
No, it didn't influence the speed of the waves.
How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances?
The speed of the waves in the 10 meter distance is
What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
The medium changed.
The wavelength changed.
The speed changed.
The frequency changed.
the wavelength, speed, and frequency
How do the speeds of the waves compare for the 2 different types of springs?
The tightly coiled high tension spring is almost twice as fast as the slinky spring.
What are some differences between the longitudinal and the transverse wave?
Longitudinal waves move parallel to the spring, and the transverse wave is perpendicular to the spring.
Summary Sound:
Method 2:
Traveling Waves: Waves that travel from one type of medium to another and transfer energy through the exchange of medium. Standing Waves: Standing waves are stationary and resonate in one medium where the amplitude and trough are at maximum displacement. This causes maximum resonance.
Sound: Sound is a mechanical wave that travels through mediums and have features such as compression and rarefaction that creates the maximum and minimum displacement. The sound can be perceived as pitch and loudness, which is frequency and amplitude. Humans can generally perceive a range of 20-20000 hz of frequency and pitch. We can measure the intensity of the sound through intensity levels of the wave of decibels.
Human Perception of Sound: Sound Wave Behavior: Sound can have features such as interference, reflection, and diffraction. All of the features apply especially the interference patterns that occur in mechanical waves. The maximum displacement would create constructive interference while the minimum displacements will create destructive interference. Through this phenomenon, beats occur. Beats is a human perception in the difference of frequency. When a frequency is off up to 10 hz, we perceive beats or a steady sound coming from the two frequencies.
Doppler Effect: The Doppler effect is another phenomenon that occurs with sound waves for the perception of the observer. An example of the doppler effect is a fast moving race car. When the race car is far away we hear compressed high frequency pitch because the sound waves are compressing in front of the race car because it is going fast.
Sonic Boom: The sonic boom is the effect of doppler effect but, the object that is causing the doppler effect is moving faster then the speed of sound. The waves compress so much that is creates a large wave of compression and sound. It can be very dangerous to the average human.
Cool Picture: We can actually see the sonic boom. Lab: Transverse Standing Waves on a String Purpose: To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string.
Materials: Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;
Procedure:
Set the frequency of the oscillator to zero. Set the amplitude to maximum.
Measure the length L of the string.
Dial up the frequency a little at a time until you acquire a standing wave. If you are careful, you should be able to get the fundamental. However, if you don’t, it’s okay… just record the correct number of antinodes along with the frequency.
Measure the wavelength.
Repeat for at least 7 different harmonics. These do not have to be consecutive.
Data Table 1: Changing harmonic number
Data Table 2: Changing Tension
Calculations: Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)
v = f * wavelength v = 11.7 * 14.38 = 168.246m/s
Calculate the tension in the string. (SHOW A SAMPLE CALC!)
F = m * g . F = 0.5 * 9.8 = 4.9N
Discussion Questions: 1. What is the name given to a point on a vibrating string at which the displacement is always zero? 2. What is the name given to a point at which the displacement is always a maximum? 3. How is the length of the string related to the wavelength for standing waves? 4. What is the longest possible wavelength for a standing wave in terms of the string length? 5. Use your graph to find the frequency for n = 20. (Try it. Does it work?)6. What is the relationship between the speed of the wave and the harmonic number?7. What is the relationship between the speed of the wave and the frequency?8. What is the relationship between the wavelength and the harmonic number?9. What is the relationship between the wavelength and the frequency?
Answer: The name of the point is called a node. The name of the maximum displacement is called the antinode. The length of the string is related to standing waves because it changes the resonant frequency. The longest possible wavelength is double the length of the string. Around 250 hz because it is a straight line. The speed of the wave is directly proportional to harmonic numbers. The speed of the wave and frequency are proportional to each other as well. The relationship between wavelength and harmonic number is that they are indirectly proportional. The relationship between the wavelength and frequency is that they are inverse square relations.
Natural Frequency: Is a frequency that an object vibrates at when struck with energy to vibrate. For example the large table sounds different than the small table.
Forced Vibration: Forced vibration occurs when an object with a certain frequency is placed against an object to vibrate at that certain frequency. An example is the tuning fork placed on to the table.
Fundamental Frequency:
The fundamental frequency is when a wave has 2 nodes with 1 antinode and a maximum amplitude. These antinodes represent a harmonic. Each harmonic is represented by N in the equation N*1/2*(lambda). Each harmonic is another octave higher in pitch.
Resonance: Resonance is the combination of the natural frequency as well as forced vibration. This makes an object vibrate at their maximum wave lengths and maximum displacement.
Open end air column:
The open end air column acts exactly like the string lab. The formula is N * 1/2 * (lambda). The open air column has two antinodes on the ends of the open air columns.
Closed end air column:
Unlike the open air column, the closed air column has a different formula which is N*1/4*(lambda). This is because the closed air columns need an anti node at the opening, and a node at the closed end of the column. This is what allows for the harmonic resonance in the closed columns.
Cool Applet:
Lab: Resonance Tubes
Objective: What is the relationship between the length of a tube and its resonant frequencies?
Hypothesis: The length of the tube changes the resonance frequencies.
GRAPH: From the data in part A, make a graph of Lexp vs. n. Add the second set of data from Part B onto the same set of axes. Create a trendline, seting the y-int = 0 and including the equation of the line and R2 value.
Calculations: 1) Calculate the speed of sound.
2) Using your data in Parts A and B, calculate the Percent Error between the Experimental Lengths and the Theoretical Lengths.
Discussion Questions For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode? There are air particles that create chaos at the end of the tube causing inaccurate measurements. Why must there be an antinode at the end of the resonance tubes? There must be an antinode at the end of the resonance tube because that is the point that creates the loudest sound, and is at the highest pressure. How long would the closed tube have to be to get the 11th harmonic? 1.47m How long would the open tube have to be to get the 10th harmonic? 2.676m Draw a figure showing the fifth resonance in a tube closed at one end. Show also how the length of the tube L5,is related to the wavelength, λ. ()()( L5 = 5*1/4* lambda Draw a figure showing the fifth resonance in an open tube. Show also how the length of the tube L5,is related to the wavelength, λ. )()()()()( L5 =5* 1/2 *lambda
Calculate the difference (|θreflected– θincident|) between the measured values of the incident angle and the reflected angle for each of the three rays and record them in the Calculations Table.
Data Table 1: Reflection
Ray
Angle of Incidence, q1
Angle of Reflection, q2
Difference in Angle
Percent Error
1
11
11.5
0.5
4.5
2
25
25
0
0
3
40
40
0
0
4
50
50
0
0
5
62
62
0
0
Analysis Questions
Are your data consistent with the law of reflection? State your answer as quantitatively as possible. Yes, most of my data was consistent with the law of reflection. Besides my first data result, all of my angles were the same as each other. The first angle was off by 0.5 the original light was 11 degrees and the reflection was 11.5.
Where is the image in a plane mirror located? It is located outside of the mirror. The mirror merely reflects the light waves that hit the mirror creating the image on the outside of the mirror.
If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be? The slope would be 1. It would be the same value as each other throughout the entire graph.
What are the characteristics of all images from plane mirrors?
The characteristics of all images from plane mirrors is that it is virtual, upright, same size, and located inside mirror the same distance from the object in front of the mirror.
Summary Light Waves and Color:
Method 2:
Wavelike behaiors of light: Light acts like waves as they have features such as interference, diffraction, and reflection such as the way waves act. Interference occurs and could be proven in a simple lab experiment with a light source and a small opening. By shining the light through the opening, the light acts in a way that occurs when waves experience interference. Diffraction occurs in lights aswell, The light bends around obstacles and shines behind the obstacle aswell. Similar to the way the waves of water reflects off of obstacles, the law of reflection applies to light waves as well.
Also light has refraction which changes the wave's velocity because the medium is different.
Two Point Source Interference: The two point source interference can be explained by how the two point ripple tank experiment had work. Constructive and destructive interference
Polarization: This phenomenon occurs when film strips act like this following image:
The light is reduced to 50% intensity when one of the layers of the polaroids are used for a light source. When another layer is placed 90 degrees to the first layer, it is changed into a 100% reduction in vision.
Color and Vision:
The Electromagnetic and Visible Spectrum:
Electromagnetic waves are waves that can travel through vacuums and have a wide range of frequencies called the electromagnetic spectrum.
Within the electromagnetic spectrum, are many different types of waves that have different characteristics. The visible light spectrum is the electromagnetic frequency that human vision can perceive.
As we can see in the image, the red waves are long and slow, while the violet waves are short and fast. The red waves have the lowest amount of energy while the violet waves have highest energy.
Reflection:
The law of reflection previously discussed during the wave chapter, also applies to the reflection of light rays in plane mirrors. Plane Mirrors:
The images formed by plane mirrors have certain characteristics.
LOST - Location: Behind Orientation:Inverted Horizontally Size: Same Type: Virtual.
The plane mirrors exhibit these characteristics because of the properties of the rays that are reflected off of the mirror.
Cool Rainbow Applet:
Sperical Mirrors:
There are two types of spherical mirrors. Concave and Convex.
These two share characteristics such as the focal length which is the point at which these mirrors concentrate the reflection of rays. The center of radius is quantitatively the value of 2 focal lengths. Also they have a vertex which is the point at which the mirror meets the principal axis at its center. Concave Mirrors:
A concave mirror is a silvered concave plane that can create images with a variety of characteristics depending on location of the object.
They follow the following specific rules true for all concave mirrors.
Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.
Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.
These two rules of reflection are illustrated in the diagram below.
Mathematically we can figure out the values such as distance of image, object, or height of image or object through these equations.
The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). The magnification equation is stated as follows:
These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.
Convex Mirrors:
A convex mirror is an opposite curve to the concaved mirror and shows different characteristics to images depending on location as well. They follow different rules than the concave mirrors which apply for all convex mirrors.
The revised rules can be stated as follows:
Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in such a manner that its extension will pass through the focal point.
Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.
Mathematically the equation and process of arithmetic is the same as the concave mirror, but the focal length or point is located on the other side. This creates a negative focal length instead of the positive one that we use during the problems for concave mirrors. Refraction of Light:
Refraction of light is a feature of the visual world that we can experience anytime. By placing objects still in air and also in water we can see refraction of light distorting the image in the water opposed to the object in the air.
Broken
This phenomenon occurs because of the refraction index of the substances that we see the light rays going through. Because Air is the fastest possible speed opposed to the speed of light, we see the best image of the object when it is in the air. When the object is placed in the water, it is slightly distorted because the speed is far slower because the index of refraction for water is higher. The relationship between speed and index of refraction can be explained through this equation:
where nmaterial = index of refraction of the material By setting this equation up we can find the angle of incidence, and refraction while we can figure out the index of refraction.
Besides mathematics we can use a graph to figure out the direction or the angle of refraction of the objects through different media. There is an easy method to memorize the directions of the objects through different material.
FST = Fast to Slow, Towards NormalIf a ray of light passes across the boundary from a material in which it travels fast into a material in which travels slower, then the light ray will bend towards the normal line.
SFA = Slow to Fast, Away From NormalIf a ray of light passes across the boundary from a material in which it travels slow into a material in which travels faster, then the light ray will bend away from the normal line.
Cool Animation:
Lab Reflection of Plane Mirror:
Objective:Demonstrate that reflection from a plane surce the angle of incidence is equal to the angle of reflection.
Data:
Ray
Angle of Incidence, q1
Angle of Reflection, q2
Difference in Angle
Percent Error
1
11
11.5
0.5
4.54%
2
25
25
0
0
3
40
40
0
0
4
50
50
0
0
5
62
62
0
0
Analysis Questions
Are your data consistent with the law of reflection? State your answer as quantitatively as possible?
Yes, most of my data shows that the law of refraction is true. The angle of reflection for my ray comparative to the actual value was off by 0.5 which created a 4.5% error. Besides this my angle of incidence compared to the angle of reflection had no differences, which proves the law of reflection.
Where is the image in a plane mirror located?
The image is projected equidistant to the object to the plane of the mirror but on the opposite side of the object, behind the mirror.
If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?
The shape would be a linear line, with a slope of 1. This is because both values on the y and x at the same rate which causes the slope to be one. What are the characteristics of all images from plane mirrors? They are virtual, inverted horizontally, behind, and same size.
Lab Curved Mirrors:
Objective: Demonstrate the focal properties of spherical reflecting surfaces
Object Distance (cm)
Focal Length (cm)
Calculated Image Distance (cm)
Experimental Image Distance
(cm)
48
5
5.5
5.4
18
5
6.9
6.6
23
10
17.7
17.3
48
10
12.6
12.6
How does the measurement of the focal point found for the convex mirror relate to the focal point found for the concave mirror?
They should have very similar values and did have similar values as well. How well did your image characteristics agree with the predicted descriptions?
It had a small error of 0.2 cms Why were you not asked to determine whether the images were real or virtual? Convex mirrors always have the a virtual image. Lab: Refraction of Light Through Glass
Objective: What is relationship between Sine of incidence angle and sine of refraction angle?
Hypothesis: The sine of incidence and the sine of refraction will be directly proportional.
Calculations
Make a graph of sin θi vs sin θr.
Use your graph of sin θi vs sin θr to find the equation of the line. Record this equation and the correlation coefficient.
Show why the slope of the line is the index of refraction of acrylic. Start with Snell’s Law, rearranging it to get it in the form of sin θi vs sin θr. (Remember that graph titles are y vs. x.)
If the index of refraction of acrylic is actually 1.50, what is the percent error? (If it is greater than 10%, you need to redo your data collection!)
Analysis Questions
1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of low optical density (air) to a medium of high optical density (acrylic)?
Choose one: always smaller, always bigger, or always constant.
Provide evidence from the lab. All of the rays were bigger angles at the angle of incidence. The first angle went from 10 degrees to 7.8 degrees.
2) How does the angle of incidence compare to the angle of refraction when light travels from a medium of high optical density (acrylic) to a medium of lower optical density (air)?
Choose one: always smaller, always bigger, or always constant.
Provide evidence from the lab. It would be the opposite way the light would enter from the glass and out into the air causing a bigger angle.
3) What would happen to a light that entered the acrylic along the normal?
The light refracted towards the normal.
The light refracted away from the normal.
The light only reflected off the plate.
The light did not refract, but went straight.
4) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
Increased.
Decreased.
Remained the same.
The slope of the equation represents the index of refraction, which was 1.39. Because the actual index of refraction was 1.52, I got a percent error of 8.5 %. The equation shows that the angle of incidence and the angle of refraction is directly proportional.
Homework: Total Internal Refraction
This picture represents an event which occcurs when a certain angle or a critical angle is reached. This critical angle prevents refraction and causes the light to be reflected directly back towards the image like a plane mirror.
Two Requirements for Total Internal Reflection
Total internal reflection (TIR) is the phenomenon that involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met:
the light is in the more dense medium and approaching the less dense medium.
the angle of incidence is greater than the so-called critical angle.
TIR
Mathematically, we can use snells law to find the critical angle. We set the refraction angle to 90 degrees. When we do this we can find either the initial angle or the index of refraction needed for the critical angle.
Table of Contents
Summary Waves:
Method 2:
Vibrations: The movement of an object in a back and forth manner. The object even at molecular level is moving in a wiggling motion causing the object to oscillate. This motion is what creates the movement of vibration. Vibration can be considered as an object being displaced out of equilibrium and passing back and forth over the original position.
Periodic Motion: Periodic motion is when an object goes under a repetitive, and constant motion. Periodic motion also deals with periods which is a length of time measured for the completion of an object's routine motion. This can be expressed as T in units and is 1/ frequency mathematically. Frequency of the periods, or the amount of times the object completes a period is called the frequency, and it can be measured by frequency = 1/period. Also within periods are amplitudes that express the maximum and minimum displacement of the object.
Simple Harmonic Motion: A motion in which acceleration of vibrating object is directly proportional to displacement and is always the same distance from the origin.
Such as the SHM spring above ^.
Pendulum Motion: The combination of centripetal force, GPE, and kinetic energy acting on an object with forces from weight and tension. Pendulum motion consists of the object moving in constant oscillation where there would be displacement horizontally as well as vertically for GPE and KE. One of the factors in pendulum motion is that the object is at it's fastest point of velocity at the bottom of the pendulum. Period of a pendulum can be measured by one complete movement of an object when the displacement returns back to 0. The object starts at the origin moves towards one side back to origin another side and back to origin. This is considered one period.
Hookes Law: The mass and the distance that the object stretches the spring is proportional to each other.
Waves:
Transverse Wave: particles of medium move in a perpendicular direction that the wave moves
Longitudinal Wave: particles of medium move in a parallel direction that the wave moves
Surface Wave: particles of medium move in a circular motion.
Electromagnetic Wave: Does not require a medium to transfer its energy.
Mechanical Wave: Does require a medium to transfer its energy.
Properties of Mechanical Waves: There are certain properties and terms that waves have, first is the crest which signifies the waves greatest amplitude, or where it has the greatest energy. The trough is the opposite, and is the position that has the least energy. Waves also deal with frequency and periods that was discussed earlier but have different equations. Wave Length is measured by 3 nodes where both crest and trough are present to create the wavelength measurement. Speed or the disturbance of the wave is measured by distance/time or frequency * wavelength,
Behavior of Waves:
Reflection: The wave bounces off of the boundary and moves in the angle of the intersection of the motion of the wave and the plane of the object.
Refraction: When the wave changes medium and most often takes on different speeds and direction.
Diffraction: When the wave hits a boundary and goes around it to conform to the shape of the object. The wave can also go through an opening and opens out in a cone shape spreading out evenly.
Interference: When 2 waves meet, it can cause either a constructive or destructive interference. Constructive interference creates a sum or a greater amplitude when the 2 waves meet. Destructive interference reduces the amplitude of the waves and creates a smaller wave when the 2 waves meet.
Doppler Effect: The doppler effect is a common phenomenon in our everyday life. An example would be a fast race car which has a distinct sound going from high to low pitch when the cars pass by. This occurs because the waves build up in front of the sound source because it is moving fast, so the observer hears a distorted sound when they are far away. The observer regains the normal sound when the car becomes closer because they don't have build up waves near or around the sides of the cars. Lastly the sound is lower as the car moves by because the sound is lagging behind causing less frequent waves.
Cool Video:
http://www.youtube.com/watch?v=DfPeprQ7oGc
Lesson: July 15, 2011
Lab: Mass on a Spring
What is the relationship between the force that a spring exerts on a mass and the distance the spring stretches?
Hypothesis:
It is a linear relationship.
Data and Graph:
Calculations:
We used the distance that the weight had stretched the spring as well as the weight for a force. Weight is calculated by 0.05 * 9.8. The force is only weight because we can only calculate that value. The distance is quantitative data that we have gathered.
Conclusion:
The relationship between distance and force is a linear relationship. It can be proven by our R^2 value of 0.999% making it a linear fit.The values or the slopes of the linear graph is the spring force constant. This is because of the formula from hooke's law. The differences between the two lines are that they have different spring force constants which changes the slope of the graphs.
Objective:
To find the relationship between wave speed and frequency.
To find the relationship between wave speed and wavelength.
To distinguish between transverse and longitudinal waves.
Hypotheses: _
_The spring will move directly proportional as more mass is added.
_
Materials: _
Procedure:
Part I – Marking the floor
Part II – Making a transverse pulse
Part III – Making a longitudinal pulse
_
Discussion Questions
- How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance?
The speed of the waves do not change too much. It seems to be relatively similar.- Did amplitude influence the speed of the waves for the 5.0 meter distance?
No it didn't influence the speed of the wave.- How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance?
The speed of 3 different amplitudes don't change.- Did amplitude influence the speed of the waves for the 10.0 meter distance?
No, it didn't influence the speed of the waves.- How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances?
The speed of the waves in the 10 meter distance is- What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
- The medium changed.
- The wavelength changed.
- The speed changed.
- The frequency changed.
the wavelength, speed, and frequency- How do the speeds of the waves compare for the 2 different types of springs?
The tightly coiled high tension spring is almost twice as fast as the slinky spring.- What are some differences between the longitudinal and the transverse wave?
Longitudinal waves move parallel to the spring, and the transverse wave is perpendicular to the spring.Summary Sound:
Method 2:
Traveling Waves: Waves that travel from one type of medium to another and transfer energy through the exchange of medium.
Standing Waves: Standing waves are stationary and resonate in one medium where the amplitude and trough are at maximum displacement. This causes maximum resonance.
Sound: Sound is a mechanical wave that travels through mediums and have features such as compression and rarefaction that creates the maximum and minimum displacement. The sound can be perceived as pitch and loudness, which is frequency and amplitude. Humans can generally perceive a range of 20-20000 hz of frequency and pitch. We can measure the intensity of the sound through intensity levels of the wave of decibels.
Human Perception of Sound:
Sound Wave Behavior: Sound can have features such as interference, reflection, and diffraction. All of the features apply especially the interference patterns that occur in mechanical waves. The maximum displacement would create constructive interference while the minimum displacements will create destructive interference. Through this phenomenon, beats occur. Beats is a human perception in the difference of frequency. When a frequency is off up to 10 hz, we perceive beats or a steady sound coming from the two frequencies.
Doppler Effect: The Doppler effect is another phenomenon that occurs with sound waves for the perception of the observer. An example of the doppler effect is a fast moving race car. When the race car is far away we hear compressed high frequency pitch because the sound waves are compressing in front of the race car because it is going fast.
Sonic Boom: The sonic boom is the effect of doppler effect but, the object that is causing the doppler effect is moving faster then the speed of sound. The waves compress so much that is creates a large wave of compression and sound. It can be very dangerous to the average human.
Cool Picture: We can actually see the sonic boom.
Lab: Transverse Standing Waves on a String
Purpose:
To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string.
Materials:
Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;
Procedure:
Data Table 1: Changing harmonic number
Data Table 2: Changing Tension
Calculations:
Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)
v = f * wavelength v = 11.7 * 14.38 = 168.246m/s
Calculate the tension in the string. (SHOW A SAMPLE CALC!)
F = m * g . F = 0.5 * 9.8 = 4.9N
Discussion Questions:
1. What is the name given to a point on a vibrating string at which the displacement is always zero? 2. What is the name given to a point at which the displacement is always a maximum? 3. How is the length of the string related to the wavelength for standing waves? 4. What is the longest possible wavelength for a standing wave in terms of the string length? 5. Use your graph to find the frequency for n = 20. (Try it. Does it work?)6. What is the relationship between the speed of the wave and the harmonic number?7. What is the relationship between the speed of the wave and the frequency?8. What is the relationship between the wavelength and the harmonic number?9. What is the relationship between the wavelength and the frequency?
Answer: The name of the point is called a node. The name of the maximum displacement is called the antinode. The length of the string is related to standing waves because it changes the resonant frequency. The longest possible wavelength is double the length of the string. Around 250 hz because it is a straight line. The speed of the wave is directly proportional to harmonic numbers. The speed of the wave and frequency are proportional to each other as well. The relationship between wavelength and harmonic number is that they are indirectly proportional. The relationship between the wavelength and frequency is that they are inverse square relations.
Summary Resonance of Sound:
Method 2:
Natural Frequency: Is a frequency that an object vibrates at when struck with energy to vibrate. For example the large table sounds different than the small table.
Forced Vibration: Forced vibration occurs when an object with a certain frequency is placed against an object to vibrate at that certain frequency. An example is the tuning fork placed on to the table.
Fundamental Frequency:
The fundamental frequency is when a wave has 2 nodes with 1 antinode and a maximum amplitude. These antinodes represent a harmonic. Each harmonic is represented by N in the equation N*1/2*(lambda). Each harmonic is another octave higher in pitch.
Resonance: Resonance is the combination of the natural frequency as well as forced vibration. This makes an object vibrate at their maximum wave lengths and maximum displacement.
Open end air column:
The open end air column acts exactly like the string lab. The formula is N * 1/2 * (lambda). The open air column has two antinodes on the ends of the open air columns.
Closed end air column:
Unlike the open air column, the closed air column has a different formula which is N*1/4*(lambda). This is because the closed air columns need an anti node at the opening, and a node at the closed end of the column. This is what allows for the harmonic resonance in the closed columns.
Cool Applet:
Lab: Resonance Tubes
Objective: What is the relationship between the length of a tube and its resonant frequencies?
Hypothesis: The length of the tube changes the resonance frequencies.
GRAPH:
From the data in part A, make a graph of Lexp vs. n. Add the second set of data from Part B onto the same set of axes. Create a trendline, seting the y-int = 0 and including the equation of the line and R2 value.
Calculations:
1) Calculate the speed of sound.
2) Using your data in Parts A and B, calculate the Percent Error between the Experimental Lengths and the Theoretical Lengths.
Discussion Questions
For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode?
There are air particles that create chaos at the end of the tube causing inaccurate measurements.
Why must there be an antinode at the end of the resonance tubes?
There must be an antinode at the end of the resonance tube because that is the point that creates the loudest sound, and is at the highest pressure.
How long would the closed tube have to be to get the 11th harmonic?
1.47m
How long would the open tube have to be to get the 10th harmonic?
2.676m
Draw a figure showing the fifth resonance in a tube closed at one end. Show also how the length of the tube L5,is related to the wavelength, λ.
()()( L5 = 5*1/4* lambda
Draw a figure showing the fifth resonance in an open tube. Show also how the length of the tube L5,is related to the wavelength, λ.
)()()()()( L5 =5* 1/2 *lambda
Lab Reflection Plane Mirror:
Analysis
Calculate the difference (|θreflected– θincident|) between the measured values of the incident angle and the reflected angle for each of the three rays and record them in the Calculations Table.Data Table 1: Reflection
Ray
Analysis Questions
Are your data consistent with the law of reflection? State your answer as quantitatively as possible.
Yes, most of my data was consistent with the law of reflection. Besides my first data result, all of my angles were the same as each other. The first angle was off by 0.5 the original light was 11 degrees and the reflection was 11.5.
Where is the image in a plane mirror located?
It is located outside of the mirror. The mirror merely reflects the light waves that hit the mirror creating the image on the outside of the mirror.
If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?
The slope would be 1. It would be the same value as each other throughout the entire graph.
What are the characteristics of all images from plane mirrors?
The characteristics of all images from plane mirrors is that it is virtual, upright, same size, and located inside mirror the same distance from the object in front of the mirror.
Summary Light Waves and Color:
Method 2:Wavelike behaiors of light: Light acts like waves as they have features such as interference, diffraction, and reflection such as the way waves act. Interference occurs and could be proven in a simple lab experiment with a light source and a small opening. By shining the light through the opening, the light acts in a way that occurs when waves experience interference. Diffraction occurs in lights aswell, The light bends around obstacles and shines behind the obstacle aswell. Similar to the way the waves of water reflects off of obstacles, the law of reflection applies to light waves as well.
Also light has refraction which changes the wave's velocity because the medium is different.
Two Point Source Interference: The two point source interference can be explained by how the two point ripple tank experiment had work. Constructive and destructive interference
Polarization: This phenomenon occurs when film strips act like this following image:
The light is reduced to 50% intensity when one of the layers of the polaroids are used for a light source. When another layer is placed 90 degrees to the first layer, it is changed into a 100% reduction in vision.
Color and Vision:
The Electromagnetic and Visible Spectrum:
Electromagnetic waves are waves that can travel through vacuums and have a wide range of frequencies called the electromagnetic spectrum.
Within the electromagnetic spectrum, are many different types of waves that have different characteristics. The visible light spectrum is the electromagnetic frequency that human vision can perceive.
As we can see in the image, the red waves are long and slow, while the violet waves are short and fast. The red waves have the lowest amount of energy while the violet waves have highest energy.
Reflection:
The law of reflection previously discussed during the wave chapter, also applies to the reflection of light rays in plane mirrors.
Plane Mirrors:
The images formed by plane mirrors have certain characteristics.
LOST - Location: Behind Orientation:Inverted Horizontally Size: Same Type: Virtual.
The plane mirrors exhibit these characteristics because of the properties of the rays that are reflected off of the mirror.
Cool Rainbow Applet:
Sperical Mirrors:
There are two types of spherical mirrors. Concave and Convex.
These two share characteristics such as the focal length which is the point at which these mirrors concentrate the reflection of rays. The center of radius is quantitatively the value of 2 focal lengths. Also they have a vertex which is the point at which the mirror meets the principal axis at its center.
Concave Mirrors:
A concave mirror is a silvered concave plane that can create images with a variety of characteristics depending on location of the object.
They follow the following specific rules true for all concave mirrors.
- Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.
- Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.
These two rules of reflection are illustrated in the diagram below.
Mathematically we can figure out the values such as distance of image, object, or height of image or object through these equations.Convex Mirrors:
A convex mirror is an opposite curve to the concaved mirror and shows different characteristics to images depending on location as well. They follow different rules than the concave mirrors which apply for all convex mirrors.The revised rules can be stated as follows:
- Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in such a manner that its extension will pass through the focal point.
- Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.
Mathematically the equation and process of arithmetic is the same as the concave mirror, but the focal length or point is located on the other side. This creates a negative focal length instead of the positive one that we use during the problems for concave mirrors.Refraction of Light:
Refraction of light is a feature of the visual world that we can experience anytime. By placing objects still in air and also in water we can see refraction of light distorting the image in the water opposed to the object in the air.
This phenomenon occurs because of the refraction index of the substances that we see the light rays going through. Because Air is the fastest possible speed opposed to the speed of light, we see the best image of the object when it is in the air. When the object is placed in the water, it is slightly distorted because the speed is far slower because the index of refraction for water is higher. The relationship between speed and index of refraction can be explained through this equation:
where nmaterial = index of refraction of the material
By setting this equation up we can find the angle of incidence, and refraction while we can figure out the index of refraction.
Besides mathematics we can use a graph to figure out the direction or the angle of refraction of the objects through different media. There is an easy method to memorize the directions of the objects through different material.
Cool Animation:
Lab Reflection of Plane Mirror:
Objective: Demonstrate that reflection from a plane surce the angle of incidence is equal to the angle of reflection.Data:
Analysis Questions
Are your data consistent with the law of reflection? State your answer as quantitatively as possible?
Yes, most of my data shows that the law of refraction is true. The angle of reflection for my ray comparative to the actual value was off by 0.5 which created a 4.5% error. Besides this my angle of incidence compared to the angle of reflection had no differences, which proves the law of reflection.
Where is the image in a plane mirror located?
The image is projected equidistant to the object to the plane of the mirror but on the opposite side of the object, behind the mirror.
If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?
The shape would be a linear line, with a slope of 1. This is because both values on the y and x at the same rate which causes the slope to be one.
What are the characteristics of all images from plane mirrors?
They are virtual, inverted horizontally, behind, and same size.
Lab Curved Mirrors:
Objective: Demonstrate the focal properties of spherical reflecting surfaces
(cm)
How does the measurement of the focal point found for the convex mirror relate to the focal point found for the concave mirror?
They should have very similar values and did have similar values as well.
How well did your image characteristics agree with the predicted descriptions?
It had a small error of 0.2 cms
Why were you not asked to determine whether the images were real or virtual?
Convex mirrors always have the a virtual image.
Lab: Refraction of Light Through Glass
Objective: What is relationship between Sine of incidence angle and sine of refraction angle?
Hypothesis: The sine of incidence and the sine of refraction will be directly proportional.
Calculations
Analysis Questions
1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of low optical density (air) to a medium of high optical density (acrylic)?
2) How does the angle of incidence compare to the angle of refraction when light travels from a medium of high optical density (acrylic) to a medium of lower optical density (air)?
3) What would happen to a light that entered the acrylic along the normal?
4) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
The slope of the equation represents the index of refraction, which was 1.39. Because the actual index of refraction was 1.52, I got a percent error of 8.5 %. The equation shows that the angle of incidence and the angle of refraction is directly proportional.
Homework: Total Internal Refraction
This picture represents an event which occcurs when a certain angle or a critical angle is reached. This critical angle prevents refraction and causes the light to be reflected directly back towards the image like a plane mirror.
Two Requirements for Total Internal Reflection
Total internal reflection (TIR) is the phenomenon that involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met:
Mathematically, we can use snells law to find the critical angle. We set the refraction angle to 90 degrees. When we do this we can find either the initial angle or the index of refraction needed for the critical angle.
Cool Animation: